Natural Construction of Ten Borcherds-Kac-Moody Algebras Associated with Elements in $M_{23}$

Abstract

Borcherds-Kac-Moody algebras generalise finite-dimensional, simple Lie algebras. Scheithauer showed that there are exactly ten Borcherds-Kac-Moody algebras whose denominator identities are completely reflective automorphic products of singular weight on lattices of square-free level. These belong to a larger class of Borcherds-Kac-Moody (super)algebras Borcherds obtained by twisting the denominator identity of the Fake Monster Lie algebra. Borcherds asked whether these Lie (super)algebras admit natural constructions. For the ten Lie algebras from the classification we give a positive answer to this question, i.e. we prove that they can be realised uniformly as the BRST cohomology of suitable vertex algebras.

34 pages, LaTeX; minor revisions, some proofs expanded, numbering changed; to appear in Comm. Math. Phys

References in corpus (3)

• Construction and Classification of Holomorphic Vertex Operator Algebras
• Lorentzian Kac-Moody algebras with Weyl groups of 2-reflections
• Cyclic orbifolds of lattice vertex operator algebras having group like fusions

Cited by in corpus (1)

• BPS Algebras in 2D String Theory